It kind of sounds like they need a raised floor. Cabling bundles can be fed into ports in the floor tiles and run the length of rooms without being exposed in a way that people would trip on them.
The main issue is that you don't have the time to pull up the flooring and then run the lines. You get the machines into the room and then into the patient ASAP, as they tend to be some of the only things keeping them alive. Think a machine that replaces heart-beat function and that you will have a hard time disconnecting.
This is what I put around the lines of my sailboat.